A graphics processing unit-accelerated meshless method for two-dimensional compressible flows

Abstract

A graphics processing unit (GPU) -accelerated meshless method is presented for solving twodimensional compressible flows over aerodynamic bodies. The Compute Unified Device Architecture (CUDA) Fortran programming model is employed to port the meshless method from central processing unit to GPU as a way of achieving efficiency, which involves implementation of CUDA kernels and management of data storage structure and thread hierarchy. The CUDA kernel subroutines are designed to meet with the point-based computing of the meshless method. The corresponding point-based data structure and thread hierarchy are constructed or manipulated in the paper by presenting two specific GPU implementations of the meshless method, which are developed for solving Navier-Stokes equations. The Jameson-Schmidt-Turkel scheme is used to estimate the flux terms of the Navier-Stokes equations and an explicit four-stage Runge-Kutta scheme is applied to update the solution at time level. After tuning the performances of the resulting two GPU-accelerated meshless solvers by changing the number of threads in a block, a set of typical flows over aerodynamic bodies are simulated for validation. Numerical results are shown in a comparison with available experimental data or computational values that appear in extant literature with an analysis of code performance. This reveals that the cost of computing time of the presented test cases is significantly reduced for both solvers without losing accuracy, while impressive speedups up to 64 times are achieved due to careful management of memory access. ARTICLE HISTORY

A GPU-accelerated implicit meshless method for compressible flows

“…In order to optimize the GPU performance, the number of threads per block for each kernel should be carefully tuned. According to our recently reported work [33], 64 threads per block is a reasonable choice for the CUDA kernels. Thus the total number of thread blocks could be determined by ( 1) / gridDim nTotalThread blockDim blockDim    (17) where nTotalThread represents the total number of threads.…”

“…This pattern is adopted in the present work so that all the threads in a half wrap map/access the global memory simultaneously with respect to the center of a meshless cloud. In reality, this means consecutive thread access consecutive memory addresses [33,34]. The computed results including Mach number contours and pressure coefficients are depicted in Fig.…”

“…A careful and delicate management is needed to ease the pressure on this scarce resource. Proper reusing of non-conflicting local variables and tuning the number of threads in a block are helpful to reduce the register pressure and to achieve the optimal performance[33].…”

Refined Meshless Local Strong Form solution of Cauchy–Navier equation on an irregular domain

“…In general, recent developments in meshless community are vivid, ranging from analyses of computer execution on different platforms [6,12], reducing computational cost by introducing a piecewise approximation [13] to implementation of more complex multi-phase flow [14], and many more. This paper extends the spectra of published papers with a generalized formulation of a local strong form meshless method, termed Meshless Local Strong Form Method (MLSM) enriched with h-refinement [15] and ability to discretize arbitrary domains [7].…”

“…In general, recent developments in meshless community are vivid, ranging from analyses of computer execution on different platforms [6,12], reducing computational cost by introducing a piecewise approximation [13] to implementation of more complex multi-phase flow [14], and many more.…”